Physics sim - Progressively destroy bridge
I've had similar problems in the past, there are just a few simple things you need to do to avoid everything exploding. Just need to set the threshold for activating to be a little higher.
When making the cell fracture make sure that you have a decent margin so that the pieces aren't inside of each other. As well as make sure that the pieces have their origins recalculated to their centers. While the margins might not look good, you can always boolean the original uncracked object out of the way later during the animation.
The most important part is to make sure that after you've made all the rigid bodies, to go to the object menu, rigid bodies, then select connect. This will add a bunch of rigid body constraints that will help keep the bridge from exploding.

Just make sure that you change the setting in the constraints to breakable so that it can actually fall apart when given enough stress. You can also quickly copy the value to all of them by selecting all the constraints with one set as the main active. Then just set the breaking to on and then right click it, a small window should appear, all you have to do is click copy to selected.